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Simplifying 3a + -5b + 5c + 2a + 3b + -1c = 0 Reorder the terms: 3a + 2a + -5b + 3b + 5c + -1c = 0 Combine like terms: 3a + 2a = 5a 5a + -5b + 3b + 5c + -1c = 0 Combine like terms: -5b + 3b = -2b 5a + -2b + 5c + -1c = 0 Combine like terms: 5c + -1c = 4c 5a + -2b + 4c = 0 Solving 5a + -2b + 4c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2b' to each side of the equation. 5a + -2b + 2b + 4c = 0 + 2b Combine like terms: -2b + 2b = 0 5a + 0 + 4c = 0 + 2b 5a + 4c = 0 + 2b Remove the zero: 5a + 4c = 2b Add '-4c' to each side of the equation. 5a + 4c + -4c = 2b + -4c Combine like terms: 4c + -4c = 0 5a + 0 = 2b + -4c 5a = 2b + -4c Divide each side by '5'. a = 0.4b + -0.8c Simplifying a = 0.4b + -0.8c
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